In class assignment
Week 4
Group 1
2023-02-11
print Student Name and roll number
cat("Student Name: Abhilash Dikshit","\n")## Student Name: Abhilash Dikshitcat("Student Roll Number: 002702209")## Student Roll Number: 002702209load data
data('ToothGrowth')
head(ToothGrowth) ## len supp dose
## 1 4.2 VC 0.5
## 2 11.5 VC 0.5
## 3 7.3 VC 0.5
## 4 5.8 VC 0.5
## 5 6.4 VC 0.5
## 6 10.0 VC 0.5Exploratory Data Analysis
summary(ToothGrowth)## len supp dose
## Min. : 4.20 OJ:30 Min. :0.500
## 1st Qu.:13.07 VC:30 1st Qu.:0.500
## Median :19.25 Median :1.000
## Mean :18.81 Mean :1.167
## 3rd Qu.:25.27 3rd Qu.:2.000
## Max. :33.90 Max. :2.000nrow(ToothGrowth)## [1] 60ncol(ToothGrowth)## [1] 3names(ToothGrowth)## [1] "len" "supp" "dose"library(GGally)## Loading required package: ggplot2## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggpairs(ToothGrowth)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
2. Comparing tooth growth by supp and dose using statistical tests
library(plotly)##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutpar(mfrow=c(2,3))
plot_ly(data=ToothGrowth, x=~supp, y=~len, type="box")Change ‘dose’ from numerical variable to factor variable
ToothGrowth$dose = factor(ToothGrowth$dose, levels=c(0.5,1.0,2.0),labels=c("low","med","high")) str(ToothGrowth)## 'data.frame': 60 obs. of 3 variables:
## $ len : num 4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
## $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
## $ dose: Factor w/ 3 levels "low","med","high": 1 1 1 1 1 1 1 1 1 1 ...Replication
replications(len ~ supp * dose, data=ToothGrowth)## supp dose supp:dose
## 30 20 10replications(len ~ supp * dose, data=ToothGrowth[1:58,])## $supp
## supp
## OJ VC
## 28 30
##
## $dose
## dose
## low med high
## 20 20 18
##
## $`supp:dose`
## dose
## supp low med high
## OJ 10 10 8
## VC 10 10 10aggregate(ToothGrowth$len, by=list(ToothGrowth$supp,ToothGrowth$dose), FUN = mean)## Group.1 Group.2 x
## 1 OJ low 13.23
## 2 VC low 7.98
## 3 OJ med 22.70
## 4 VC med 16.77
## 5 OJ high 26.06
## 6 VC high 26.14aggregate(ToothGrowth$len, by=list(ToothGrowth$supp,ToothGrowth$dose), FUN = sd)## Group.1 Group.2 x
## 1 OJ low 4.459709
## 2 VC low 2.746634
## 3 OJ med 3.910953
## 4 VC med 2.515309
## 5 OJ high 2.655058
## 6 VC high 4.797731dose <- factor(ToothGrowth$dose)
fit <- aov(ToothGrowth$len ~ ToothGrowth$supp*ToothGrowth$dose)
summary(fit)## Df Sum Sq Mean Sq F value Pr(>F)
## ToothGrowth$supp 1 205.4 205.4 15.572 0.000231 ***
## ToothGrowth$dose 2 2426.4 1213.2 92.000 < 2e-16 ***
## ToothGrowth$supp:ToothGrowth$dose 2 108.3 54.2 4.107 0.021860 *
## Residuals 54 712.1 13.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1dose <- factor(dose)
fit <- aov(ToothGrowth$len ~ ToothGrowth$supp*ToothGrowth$dose)
summary(fit)## Df Sum Sq Mean Sq F value Pr(>F)
## ToothGrowth$supp 1 205.4 205.4 15.572 0.000231 ***
## ToothGrowth$dose 2 2426.4 1213.2 92.000 < 2e-16 ***
## ToothGrowth$supp:ToothGrowth$dose 2 108.3 54.2 4.107 0.021860 *
## Residuals 54 712.1 13.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Graphical Explanation
Box Plot
boxplot(len ~ supp * dose, data=ToothGrowth, ylab="Tooth Length", main="Boxplots of Tooth Growth Data", col= "skyblue")
Interaction Plot
with(ToothGrowth, interaction.plot(x.factor=dose, trace.factor=supp,response=len, fun=mean, type="b", legend=T,ylab="Tooth Length", main="Interaction Plot",pch=c(1,19)))
Conditional Plot
coplot(len ~ dose | supp, data=ToothGrowth, panel=panel.smooth,xlab="ToothGrowth data: length vs dose, given type of supplement", col= "red")
Using model.tables() function
aov.out = aov(len ~ supp * dose, data=ToothGrowth)model.tables(aov.out, type="means", se=T)## Tables of means
## Grand mean
##
## 18.81333
##
## supp
## supp
## OJ VC
## 20.663 16.963
##
## dose
## dose
## low med high
## 10.605 19.735 26.100
##
## supp:dose
## dose
## supp low med high
## OJ 13.23 22.70 26.06
## VC 7.98 16.77 26.14
##
## Standard errors for differences of means
## supp dose supp:dose
## 0.9376 1.1484 1.6240
## replic. 30 20 10summary(aov.out)## Df Sum Sq Mean Sq F value Pr(>F)
## supp 1 205.4 205.4 15.572 0.000231 ***
## dose 2 2426.4 1213.2 92.000 < 2e-16 ***
## supp:dose 2 108.3 54.2 4.107 0.021860 *
## Residuals 54 712.1 13.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Treatment Contrasts
options("contrasts")## $contrasts
## unordered ordered
## "contr.treatment" "contr.poly"summary.lm(aov.out)##
## Call:
## aov(formula = len ~ supp * dose, data = ToothGrowth)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.20 -2.72 -0.27 2.65 8.27
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.230 1.148 11.521 3.60e-16 ***
## suppVC -5.250 1.624 -3.233 0.00209 **
## dosemed 9.470 1.624 5.831 3.18e-07 ***
## dosehigh 12.830 1.624 7.900 1.43e-10 ***
## suppVC:dosemed -0.680 2.297 -0.296 0.76831
## suppVC:dosehigh 5.330 2.297 2.321 0.02411 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.631 on 54 degrees of freedom
## Multiple R-squared: 0.7937, Adjusted R-squared: 0.7746
## F-statistic: 41.56 on 5 and 54 DF, p-value: < 2.2e-16Conclusion of the Hypothesis Testing
The mean of the OJ-low cell: We find this mean to be significantly different from zero, not an especially interesting result. The next line of the table, “suppVC”, shows the difference between the means of the VC-low cell and the OJ-low cell.
The standard error is for the difference between these means, so the difference is found to be significant. The “dosemed” line shows the difference between the means of the OJ-med cell and the OJ-low cell, and once again this difference is found to be statistically significant. The “dosehigh” line shows the difference in means between the OJ-high cell and the OJ-low cell, also significant. The last two lines test various elements of the interaction.
Appendix
cat("Student Name: Abhilash Dikshit","\n")
cat("Student Roll Number: 002702209")
data('ToothGrowth')
head(ToothGrowth)
summary(ToothGrowth)
nrow(ToothGrowth)
ncol(ToothGrowth)
names(ToothGrowth)
library(GGally)
ggpairs(ToothGrowth)
library(plotly)
par(mfrow=c(2,3))
plot_ly(data=ToothGrowth, x=~supp, y=~len, type="box")
ToothGrowth$dose = factor(ToothGrowth$dose, levels=c(0.5,1.0,2.0),labels=c("low","med","high"))
str(ToothGrowth)
replications(len ~ supp * dose, data=ToothGrowth)
replications(len ~ supp * dose, data=ToothGrowth[1:58,])
aggregate(ToothGrowth$len, by=list(ToothGrowth$supp,ToothGrowth$dose), FUN = mean)
aggregate(ToothGrowth$len, by=list(ToothGrowth$supp,ToothGrowth$dose), FUN = sd)
dose <- factor(ToothGrowth$dose)
fit <- aov(ToothGrowth$len ~ ToothGrowth$supp*ToothGrowth$dose)
summary(fit)
dose <- factor(dose)
fit <- aov(ToothGrowth$len ~ ToothGrowth$supp*ToothGrowth$dose)
summary(fit)
boxplot(len ~ supp * dose, data=ToothGrowth, ylab="Tooth Length", main="Boxplots of Tooth Growth Data", col= "skyblue")
with(ToothGrowth, interaction.plot(x.factor=dose, trace.factor=supp,response=len, fun=mean, type="b", legend=T,ylab="Tooth Length", main="Interaction Plot",pch=c(1,19)))
coplot(len ~ dose | supp, data=ToothGrowth, panel=panel.smooth,xlab="ToothGrowth data: length vs dose, given type of supplement", col= "red")
aov.out = aov(len ~ supp * dose, data=ToothGrowth)
model.tables(aov.out, type="means", se=T)
summary(aov.out)
options("contrasts")
summary.lm(aov.out)
## NA